Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C3⋊#6157 |
| unambiguous semidirect product | C3⋊(C19⋊C3×#6157) |
| unambiguous semidirect product | (C19×C3⋊#6157)⋊C3 |
| Fitting, socle, derived | C3×C19×C53 ⋊ C3×C4 |
| Hall | C3×C53×C19⋊C3 ⋊ C4 |
| Hall | C19×C53 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ #6157 |
| Sylow | C53 ⋊ Dic3×C19⋊C3 |
| Sylow | C19 ⋊ C3×C3⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C53 | C3×C4 |
| prime radical | C3×C19⋊C3×D53 | C2 |
| cosocle | C3×C19×D53 | C2×C3 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 81);